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<div class="title">jama_lu.h</div>  </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="preprocessor">#ifndef JAMA_LU_H</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="preprocessor"></span><span class="preprocessor">#define JAMA_LU_H</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="preprocessor"></span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="preprocessor">#include &quot;tnt.h&quot;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="preprocessor">#include &lt;algorithm&gt;</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">//for min(), max() below</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;</div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="keyword">using namespace </span>TNT;</div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="keyword">using namespace </span>std;</div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;</div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="keyword">namespace </span>JAMA</div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;{</div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;</div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">class</span> Real&gt;</div>
<div class="line"><a name="l00027"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_l_u.html">   27</a></span>&#160;<span class="keyword">class </span><a class="code" href="class_j_a_m_a_1_1_l_u.html">LU</a></div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;{</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;</div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;</div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;   <span class="comment">/* Array for internal storage of decomposition.  */</span></div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;   <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a>  LU_;</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;   <span class="keywordtype">int</span> m, n, pivsign; </div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;   <a class="code" href="class_t_n_t_1_1_array1_d.html">Array1D&lt;int&gt;</a> piv;</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;   <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a> permute_copy(<span class="keyword">const</span> <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a> &amp;A, </div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;                        <span class="keyword">const</span> <a class="code" href="class_t_n_t_1_1_array1_d.html">Array1D&lt;int&gt;</a> &amp;piv, <span class="keywordtype">int</span> j0, <span class="keywordtype">int</span> j1)</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;        {</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;                <span class="keywordtype">int</span> piv_length = piv.<a class="code" href="class_t_n_t_1_1_array1_d.html#aa1c3e474d22bc02470e0a046b70c1cd1">dim</a>();</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;                <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a> X(piv_length, j1-j0+1);</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; piv_length; i++) </div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = j0; j &lt;= j1; j++) </div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;               X[i][j-j0] = A[piv[i]][j];</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;                <span class="keywordflow">return</span> X;</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;        }</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;   <a class="code" href="class_t_n_t_1_1_array1_d.html">Array1D&lt;Real&gt;</a> permute_copy(<span class="keyword">const</span> <a class="code" href="class_t_n_t_1_1_array1_d.html">Array1D&lt;Real&gt;</a> &amp;A, </div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;                <span class="keyword">const</span> <a class="code" href="class_t_n_t_1_1_array1_d.html">Array1D&lt;int&gt;</a> &amp;piv)</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;        {</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;                <span class="keywordtype">int</span> piv_length = piv.<a class="code" href="class_t_n_t_1_1_array1_d.html#aa1c3e474d22bc02470e0a046b70c1cd1">dim</a>();</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;                <span class="keywordflow">if</span> (piv_length != A.<a class="code" href="class_t_n_t_1_1_array1_d.html#aa1c3e474d22bc02470e0a046b70c1cd1">dim</a>())</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;                        <span class="keywordflow">return</span> <a class="code" href="class_t_n_t_1_1_array1_d.html">Array1D&lt;Real&gt;</a>();</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;                <a class="code" href="class_t_n_t_1_1_array1_d.html">Array1D&lt;Real&gt;</a> x(piv_length);</div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; piv_length; i++) </div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;               x[i] = A[piv[i]];</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;                <span class="keywordflow">return</span> x;</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;        }</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;        <span class="keyword">public</span> :</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;</div>
<div class="line"><a name="l00077"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_l_u.html#af280c292fc2801a6fa5e5c0a84f15685">   77</a></span>&#160;    <a class="code" href="class_j_a_m_a_1_1_l_u.html">LU</a> (<span class="keyword">const</span> <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a> &amp;A) : LU_(A.copy()), m(A.dim1()), n(A.dim2()), </div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;                piv(A.dim1())</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;        </div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;        {</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;   <span class="comment">// Use a &quot;left-looking&quot;, dot-product, Crout/Doolittle algorithm.</span></div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; m; i++) {</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;         piv[i] = i;</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;      }</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;      pivsign = 1;</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;      Real *LUrowi = 0;;</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;      <a class="code" href="class_t_n_t_1_1_array1_d.html">Array1D&lt;Real&gt;</a> LUcolj(m);</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;      <span class="comment">// Outer loop.</span></div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;         <span class="comment">// Make a copy of the j-th column to localize references.</span></div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; m; i++) {</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;            LUcolj[i] = LU_[i][j];</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;         }</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;         <span class="comment">// Apply previous transformations.</span></div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; m; i++) {</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;            LUrowi = LU_[i];</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;            <span class="comment">// Most of the time is spent in the following dot product.</span></div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;            <span class="keywordtype">int</span> kmax = min(i,j);</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;            <span class="keywordtype">double</span> s = 0.0;</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k &lt; kmax; k++) {</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;               s += LUrowi[k]*LUcolj[k];</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;            }</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;            LUrowi[j] = LUcolj[i] -= s;</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;         }</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;   </div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;         <span class="comment">// Find pivot and exchange if necessary.</span></div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;         <span class="keywordtype">int</span> p = j;</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = j+1; i &lt; m; i++) {</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;            <span class="keywordflow">if</span> (abs(LUcolj[i]) &gt; abs(LUcolj[p])) {</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;               p = i;</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;            }</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;         }</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;         <span class="keywordflow">if</span> (p != j) {</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;                    <span class="keywordtype">int</span> k=0;</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;            <span class="keywordflow">for</span> (k = 0; k &lt; n; k++) {</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;               <span class="keywordtype">double</span> t = LU_[p][k]; </div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;                           LU_[p][k] = LU_[j][k]; </div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;                           LU_[j][k] = t;</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;            }</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;            k = piv[p]; </div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;                        piv[p] = piv[j]; </div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;                        piv[j] = k;</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;            pivsign = -pivsign;</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;         }</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;         <span class="comment">// Compute multipliers.</span></div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;         </div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;         <span class="keywordflow">if</span> ((j &lt; m) &amp;&amp; (LU_[j][j] != 0.0)) {</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = j+1; i &lt; m; i++) {</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;               LU_[i][j] /= LU_[j][j];</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;            }</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;         }</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;      }</div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;   }</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;</div>
<div class="line"><a name="l00155"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_l_u.html#afc7269c15f48fbbefdcb067bf71cc179">  155</a></span>&#160;   <span class="keywordtype">int</span> <a class="code" href="class_j_a_m_a_1_1_l_u.html#afc7269c15f48fbbefdcb067bf71cc179">isNonsingular</a> () {</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;         <span class="keywordflow">if</span> (LU_[j][j] == 0)</div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;            <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;      }</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;      <span class="keywordflow">return</span> 1;</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;   }</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;</div>
<div class="line"><a name="l00167"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_l_u.html#a34b9bc8eef3f7771de20176b807bf977">  167</a></span>&#160;   <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a> <a class="code" href="class_j_a_m_a_1_1_l_u.html#a34b9bc8eef3f7771de20176b807bf977">getL</a> () {</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;      <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a> L_(m,n);</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; m; i++) {</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;            <span class="keywordflow">if</span> (i &gt; j) {</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;               L_[i][j] = LU_[i][j];</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;            } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (i == j) {</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;               L_[i][j] = 1.0;</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;            } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;               L_[i][j] = 0.0;</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;            }</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;         }</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;      }</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;      <span class="keywordflow">return</span> L_;</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;   }</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;</div>
<div class="line"><a name="l00187"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_l_u.html#ad2148238b7e2c6a2db01985cb66f8f72">  187</a></span>&#160;   <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a> <a class="code" href="class_j_a_m_a_1_1_l_u.html#ad2148238b7e2c6a2db01985cb66f8f72">getU</a> () {</div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;          <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a> U_(n,n);</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; i++) {</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;            <span class="keywordflow">if</span> (i &lt;= j) {</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;               U_[i][j] = LU_[i][j];</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;            } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;               U_[i][j] = 0.0;</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;            }</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;         }</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;      }</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;      <span class="keywordflow">return</span> U_;</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;   }</div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;</div>
<div class="line"><a name="l00205"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_l_u.html#a94dba52c7036cb779427106e65d85f1d">  205</a></span>&#160;   <a class="code" href="class_t_n_t_1_1_array1_d.html">Array1D&lt;int&gt;</a> <a class="code" href="class_j_a_m_a_1_1_l_u.html#a94dba52c7036cb779427106e65d85f1d">getPivot</a> () {</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;      <span class="keywordflow">return</span> piv;</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;   }</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;</div>
<div class="line"><a name="l00214"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_l_u.html#a954d514e3e802da2fc8a422d15df5cfd">  214</a></span>&#160;   Real <a class="code" href="class_j_a_m_a_1_1_l_u.html#a954d514e3e802da2fc8a422d15df5cfd">det</a> () {</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;      <span class="keywordflow">if</span> (m != n) {</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;         <span class="keywordflow">return</span> Real(0);</div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;      }</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;      Real d = Real(pivsign);</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;         d *= LU_[j][j];</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;      }</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;      <span class="keywordflow">return</span> d;</div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;   }</div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;</div>
<div class="line"><a name="l00231"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_l_u.html#abf011e4d8405ec35412a7fc06bd7c9a8">  231</a></span>&#160;   <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a> solve (<span class="keyword">const</span> <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a> &amp;B) </div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;   {</div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;          <span class="comment">/* Dimensions: A is mxn, X is nxk, B is mxk */</span></div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;      </div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;      <span class="keywordflow">if</span> (B.<a class="code" href="class_t_n_t_1_1_array2_d.html#a3997cd7973cd903cc46c0bd7abde03c0">dim1</a>() != m) {</div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;                <span class="keywordflow">return</span> <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a>(0,0);</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;      }</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;      <span class="keywordflow">if</span> (!isNonsingular()) {</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;        <span class="keywordflow">return</span> <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a>(0,0);</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;      }</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;      <span class="comment">// Copy right hand side with pivoting</span></div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;      <span class="keywordtype">int</span> nx = B.<a class="code" href="class_t_n_t_1_1_array2_d.html#a6efd5ac98f02bb42340be1d5cbf4c9c1">dim2</a>();</div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;</div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;</div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;          <a class="code" href="class_t_n_t_1_1_array2_d.html">Array2D&lt;Real&gt;</a> X = permute_copy(B, piv, 0, nx-1);</div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;</div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;      <span class="comment">// Solve L*Y = B(piv,:)</span></div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k &lt; n; k++) {</div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = k+1; i &lt; n; i++) {</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; nx; j++) {</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;               X[i][j] -= X[k][j]*LU_[i][k];</div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;            }</div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;         }</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;      }</div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;      <span class="comment">// Solve U*X = Y;</span></div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = n-1; k &gt;= 0; k--) {</div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; nx; j++) {</div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;            X[k][j] /= LU_[k][k];</div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;         }</div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; k; i++) {</div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;            <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; nx; j++) {</div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;               X[i][j] -= X[k][j]*LU_[i][k];</div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;            }</div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;         }</div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;      }</div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;      <span class="keywordflow">return</span> X;</div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;   }</div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;</div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;</div>
<div class="line"><a name="l00281"></a><span class="lineno"><a class="code" href="class_j_a_m_a_1_1_l_u.html#abe62763addfd25c019f09b5420198d33">  281</a></span>&#160;   <a class="code" href="class_t_n_t_1_1_array1_d.html">Array1D&lt;Real&gt;</a> solve (<span class="keyword">const</span> <a class="code" href="class_t_n_t_1_1_array1_d.html">Array1D&lt;Real&gt;</a> &amp;b) </div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;   {</div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;</div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;          <span class="comment">/* Dimensions: A is mxn, X is nxk, B is mxk */</span></div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;      </div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;      <span class="keywordflow">if</span> (b.<a class="code" href="class_t_n_t_1_1_array1_d.html#ad0e3ae296c57454d4244f44076cd1e02">dim1</a>() != m) {</div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;                <span class="keywordflow">return</span> <a class="code" href="class_t_n_t_1_1_array1_d.html">Array1D&lt;Real&gt;</a>();</div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;      }</div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;      <span class="keywordflow">if</span> (!isNonsingular()) {</div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;        <span class="keywordflow">return</span> <a class="code" href="class_t_n_t_1_1_array1_d.html">Array1D&lt;Real&gt;</a>();</div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;      }</div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;</div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;</div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;          <a class="code" href="class_t_n_t_1_1_array1_d.html">Array1D&lt;Real&gt;</a> x = permute_copy(b, piv);</div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;</div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;      <span class="comment">// Solve L*Y = B(piv)</span></div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k &lt; n; k++) {</div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = k+1; i &lt; n; i++) {</div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;               x[i] -= x[k]*LU_[i][k];</div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;            }</div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;         }</div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;      </div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;          <span class="comment">// Solve U*X = Y;</span></div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;      <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = n-1; k &gt;= 0; k--) {</div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;            x[k] /= LU_[k][k];</div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;                <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; k; i++) </div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;                x[i] -= x[k]*LU_[i][k];</div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;      }</div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;     </div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;</div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;      <span class="keywordflow">return</span> x;</div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;   }</div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;</div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;}; <span class="comment">/* class LU */</span></div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;</div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;} <span class="comment">/* namespace JAMA */</span></div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;</div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;<span class="preprocessor"></span><span class="comment">/* JAMA_LU_H */</span></div>
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